Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	277×	body	80	valid
4.0ms	101×	body	80	nan

simplify74.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma z z (- (* a t)))
1.0b	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
8.8b	(/ (* z y) (sqrt (fma z z (- (* a t)))))
23.4b	(sqrt (fma z z (- (* a t))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `sqrt-prod`
10×	`associate-l`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `associate-/l*` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

1.0ms	(fma z z (- (* a t)))
40.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
17.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
8.0ms	(sqrt (fma z z (- (* a t))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma z z (- (* a t)))
155.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
83.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
119.0ms	(sqrt (fma z z (- (* a t))))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1731
1	312
0	130

prune767.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.0b	(* (/ y (/ (sqrt (- (* z z) (* t a))) z)) x)
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`*-un-lft-identity` `add-cube-cbrt`
71×	`associate-l`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 237

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
90.0ms	(* (/ y (/ (sqrt (- (* z z) (* t a))) z)) x)
27.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
19.0ms	(sqrt (- (* z z) (* t a)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
152.0ms	(* (/ y (/ (sqrt (- (* z z) (* t a))) z)) x)
89.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

249 → 249

Iterations

Iter	Nodes
done	5000
2	4770
1	913
0	332

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1 z) (sqrt (fma (- a) t (* z z))))
1.0b	(* (* y (/ (* 1 z) (sqrt (fma (- a) t (* z z))))) x)
1.2b	(* y (/ (* 1 z) (sqrt (fma (- a) t (* z z)))))
23.4b	(sqrt (fma (- a) t (* z z)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
32×	`add-cbrt-cube`
19×	`prod-exp`
17×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r` `cbrt-unprod`
12×	`pow1` `times-frac` `sqrt-prod`
9×	`div-exp`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`1-exp`
2×	`associate-r/` `-commutative` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/l` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

17.0ms	(/ (* 1 z) (sqrt (fma (- a) t (* z z))))
86.0ms	(* (* y (/ (* 1 z) (sqrt (fma (- a) t (* z z))))) x)
34.0ms	(* y (/ (* 1 z) (sqrt (fma (- a) t (* z z)))))
1.0ms	(sqrt (fma (- a) t (* z z)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (* 1 z) (sqrt (fma (- a) t (* z z))))
149.0ms	(* (* y (/ (* 1 z) (sqrt (fma (- a) t (* z z))))) x)
97.0ms	(* y (/ (* 1 z) (sqrt (fma (- a) t (* z z)))))
115.0ms	(sqrt (fma (- a) t (* z z)))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1910
1	363
0	143

prune794.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize55.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (/ z (sqrt (fma t (- a) (* z z)))))
23.4b	(sqrt (fma (- a) t (* z z)))
23.4b	(sqrt (fma t (- a) (* z z)))
23.4b	(sqrt (fma t (- a) (* z z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 78

Calls

4 calls:

6.0ms	(cbrt (/ z (sqrt (fma t (- a) (* z z)))))
2.0ms	(sqrt (fma (- a) t (* z z)))
2.0ms	(sqrt (fma t (- a) (* z z)))
3.0ms	(sqrt (fma t (- a) (* z z)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (/ z (sqrt (fma t (- a) (* z z)))))
114.0ms	(sqrt (fma (- a) t (* z z)))
130.0ms	(sqrt (fma t (- a) (* z z)))
129.0ms	(sqrt (fma t (- a) (* z z)))

simplify977.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	1274
2	431
1	209
0	137

prune932.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.0b

regimes915.0ms

Accuracy

84% (3.1b remaining)

Error of 6.3b against oracle of 3.1b and baseline of 22.6b

bsearch158.0ms

Steps

Iters	Range		Point
9	9.954194639794559e+62	3.050813620623569e+72	2.235109143959164e+72
7	-3.4958908093813164e+126	-3.425023176292938e+124	-2.558831417467723e+125

simplify10.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	33

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	8798×	body	80	valid
342.0ms	2980×	body	80	nan